The Verizon Galaxy Note II now has root, thanks to some folks over at XDA. It looks like it's a fairly easy and straightforward affair, using ODIN. As always, be careful with the process and follow the instructions carefully. It's important to note that there are still some bugs to be worked out with this one, and of course, the phone is still locked. Still, those details will likely be hammered out fairly soon. Here's a quote with the instructions below. Be sure to hit up the source link for additional details and downloads.

Section 1: How to Root/ Return to stock Stock 4.1.1 JellyBean with Odin

Step 3: Power device off, hold the volume down/home/power keys until you see a yellow triangle, then press the volume up key to access "odin or download mode".

Step 4: Open odin and connect the oem usb cable from pc to device. Adb driver should automatically install(atleast it did for me on windows 7). There should be a "comport number" in upper left hand corner of odin indicating communication between the pc & device.

Step 5: Uncheck Auto reboot

Step 6: Click on the PDA function of odin. Select the rooted system.img you downloaded in step 2, then select start. This operation should take less than 8 minutes before odin will say pass/reset.

Step 7: Pull and reinstall battery.

Step 8: Press and hold the volume up/home/power buttons until you see a green android. You should boot into ASR(Android Stock Recovery)

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